Linked cluster expansions beyond nearest neighbour interactions: convergence and graph classes

Abstract

We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way that the classes of graphs to be considered are identical to those of the pure nearest neighbour interaction. The only change then concerns the computation of lattice imbedding numbers. All the complications that arise can be reduced to a generalization of the notion of free random walks, including hopping beyond nearest neighbour. Explicit expressions for combinatorical numbers of the latter are given. We show that under some general conditions the linked cluster expansion series have a non-vanishing radius of convergence.

20 pages, latex2e

References in corpus (4)

• New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices
• Advanced Linked Cluster Expansion. Scalar Fields at Finite Temperature
• Strong-coupling expansion of lattice O(N) sigma models
• A Convergence Proof for Linked Cluster Expansions

Cited by in corpus (5)

• The Gross-Neveu model and QCDs chiral phase transition
• Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions
• Graph rules for the linked cluster expansion of the Legendre effective action
• Hopping Parameter Series Construction for Models with Nontrivial Vacuum
• Linked Cluster Expansions on non-trivial topologies